I was struggling today with this question: does a free photon have a continuous energy spectra?
Free means in no context of any energy system (eg. an atom, em field). Although I'm asking myself if the quantization of the electromagnetic field is omnipresent and will always make the energy discrete?
Edit: This leads me also to the question: if we have 2 energy levels (like in hydrogen: ground state and first excited) the uncertainty principle tells us, that the energy isn't quite exact defined: $\Delta E\Delta t \ge \hbar$ . Therefore the final energy of the emitted photon won't have a discrete energy, since it would be sth. like $E_{photon} = E_{0} + \Delta E$ ?!
Answer
A free particle (photon, electron etc) is not restricted to discrete energy levels. Its wavelength and therefore energy can take any value. A plane wave, with any wavelength you choose, can satisfy the Schrodinger equation for a single free particle.
A free particle does not have to have a single precise energy. For example, a wave packet (a quantum wave that moves along like a fizzy ball) in free space has a range of energies.
A particle that is confined will have discrete energy levels. For example, an electron in orbit around a nucleus.
So quantum mechanics does not always mean that energy or any other property is "quantized".
No comments:
Post a Comment